PERIOD
DATE
Lesson
I Reteath
Rotatfons
A rotation is a transformation in which a figure is rotated, or turned, about a fixed point. The center of
rotation is the fixed point. The preimage and the image are congruent.
Example t
Tbiangle ABC has vertices A(8, 2), B(5, 4), C(6,2r. Graph the frgure and its image
after a counterclockwise rotation of g0' about vertex A. Then give the coordinates
of the vertices for A'B'C'.
Step 1
Graph the original triangle.
Step
2
Graph the rotated image. Use a protractor
to measure an angle of 90' with B as one
point on the ray and A as the vertex. Mark
off a point the same distance as BA. Label
this point B'as shown.
Step
3
Repeat Step 2 for point C. Since A is the
point at which AABC is rotated,A'will be
in the same position as A.
So,
.i
E
the coordinates of the vertices of LABC are A'(3,2), B'(1, 4), C'(3,5).
Example 2
TYiangle GHI }nas vertices G(L, 2), H (3, 5), I (3, 2). Graph the frgure and its image
after a clockwise rotation of 9O" about the origin. Then give the coordinates of the
vertices for AG'H'I'.
I
Step 2
Step
I
.9
.9
E
Step
.9
E
So,
3
Graph LGHI on a coordinate plane.
Sketch Gocot.tecting point G
to the origin. Sketch another segment, G'O'
so that the angle between point G, O, and
G'measures 90" and the segment is
congruent to GO.
Repeat Step 2 for points H and,I. Then
connect the vertices to form AG'H'I'.
the coordinates of the vertices of AG'H'I' are G'(2,
-l),
H'(5, -3), and I'(2, -3).
g
=
Exercises
2
Refer to AGHI in Example 2 above. Graph GHI after each rotation.
Then give the coordinates of the vertices for G'H'I'.
F
t
1. 180o counterclockwise about vertex G
2. 180" clockwise about the origin
Course
I . Chapter 6 Transformations
95
PERIOD
DATE
lesson
I Skills Practice
Rotations
For Exercises 1. and 2, graph AWZ and its image after eaeh
rotation. Then give the coordinates of the vertices for AXY'Z'.
r
1. 180" clockwise about vertex Z
2. 90' clockwise about vertex X
o
I
=
6
€
3. TYiangle JKL has vertices J(-4,4), K(-1,3), and
L(-2,1). Graph the figure and its rotated image after a
clockwise rotation of 90" about the origin. Then give the
coordinates of the vertices for triangle J'K'L'.
3
6'
I
3
a'
a'
4. Quadrilateral BCDE has vertices B(3, 6), C(6, 5), D(5,2),
and E(2,3). Graph the frgure and its rotated image after
a
a counterclockwise rotation of 180" about the origin.
Then give the coordinates ofthe vertices for quadrilateral
B'C'D'E'.
:
-4 c
4
8x
6.
3
jD
96
Course
I . Chapter 6 Transformations
NAME
PERIOD
Lesson 3 Extra Practice
Rotations
Triangle XY Z has vertices at X(3, 1), YQ, 7), and. Z(7, l). Graph
triangle XYZ and its image after each rotation. Then give the
coordinates of the vertices of the image.
1. 180" counterclockwise
3. 180'clockwise
Course
3.
Chapter
about vertex
about the origin
6
Transformations
X
2.
90" clockwise aboutvertexZ
4. 27A" counterclockwise
about the origin
PERIOD
DATE
Lesson x Reteach
Rotations
A rotation is a transformation in which a figure is rotated, or turned, about a fixed point. The center o{
rotation is the fixed point. The preimage and the image are congruent.
Example I
Thiangle ABC has vertices A(3r 2'), B(5, 4>, C(6,2'). Graph the frgure and its image
after a eounterclockwise rotation of 90' about vertex A. Then give the eoordinates
of the vertices for A'B'C',
I
Step 2
Step
Step
So,
4
E
3
.9
Step 3
So,
o
=
F
6
Repeat Step 2 for point C. Since A is the
point at which AABC is rotated, A'will be
in the same position as A.
Example 2
Tbiangle GHIhas vertices G(1,2),II(3,5), I(3,2). Graph the frgure and its image
after a clockwise rotation of 90' about the origin. Then give the coordinates of the
vertices fot LG'H'I'.
1
Step 2
-3
Graph the rotated image. Use a protractor
to measure an angle of 90' with B as one
point on the ray and A as the vertex. Mark
off a point the same distance as B.[. Label
this point B'as shown.
the coordinates of the vertices of LABC are A'(3,2), B'(1, 4), C'(3, 5).
Step
E
Graph the original triangle.
Graph LGHI on a coordinate plane.
Sketch GO connecting point G
to the origin. Sketch another segment, G'O'
so that the angle between point G, O, and
G'measures 90' and the segment is
congruent to GO.
Repeat Step 2 for points H and.I. Then
connect the vertices to form LG'H'I'.
the coordinates of the vertices of AG'H'I' are G'(2, *7), H'(5, -B), and I'{2, -3).
Exercises
Refer to AGHI in Example 2 ahove. Graph GHI after each rotation.
Then give the coordinates of the vertices for G'H'I',
See students'graphs.
L. 180'counterclockwise about vertex G G'(1,21, H'(-1, -l), l'(-1r2t
2. 180' clockwise about the origin G(-1 ,
-2), H'(-3, -5), ,'(-3 ,
Coufse
3 . Chapter 6
Transformations
-Z)
95
DATE
PERIOD
Lesson 5 Skills Pradice
Fotatlons
For Exercises
I and 2, graph
AXYZ and its image after each
rotation.Ihen give the coordinates of the vertices for AXY'Z'.
1. 180' clochrise about vertex Z
x'(6,1),Y',(4, -4), Z',(2, -11
2. 90' clockwise about vertex X
x'(-2,
-l),
y'(1,
-3), z'(-2, -5)
fi'
o
3. Triangle JKL
}l.as vertices
J(-4,
4),
K(-1,3),
=
and
L(-2,1). Graph the figure and its rotated image after
d
f
a
+J+t"tI+-+#
clockwise rotation of 90" about the origin. Then give the
coordinates of the vertices for triangle J'K'L'.
=
;'
a
!
J'(4,4), K'(3,1), and L'(1,2'l
1
9.
a
4. Quadrilateral BCDE has vertices B(3, 6), C(6, 5), D(5,2),
and E(2,3). Graph the frgure and its rotated image after
a counterclockwise rotation of 180' about the origin.
Then give the coordinates of the vertices for quadrilateral
a
!
B'C'D'E'.
:4
4
8.r
B'(-3, -6), C'(-6, -5), D'(-5, -2), and E'(-2, -O)
96
Course
a
3
P
I . Chapter 6 Transformations
6-3
Z(7,l)
,Y(3, 1), Y(3, -5), Z',(*l , 1)
x(7,
x (-3, -1), r(-3, -7), Z', (-7, -1)
x(1, *3), Y(7, -3), Z(1, -7)
Course
3.
Chapter
6
Transformations
5), Y(13,5),